The Algebra Problem

Research shows that students who complete a mathematics course beyond the level of Algebra II more than double the odds of pursuing and completing post-secondary education (Adelman, 1999). Many districts now require completion of an Algebra I course prior to completion of 9th grade (Loveless, 2008). In California, many students are failing Algebra.  In fact according to an Edsource (2011) report of those students who were enrolled in 8th grade Algebra 1, nearly one-third of  students scored "below basic" or "far below basic".  Across the country failure of Algebra can run as high as fifty percent, such an alarming statistics calls into question how Algebra is taught and moreover how students are prepared.



There is little agreement as to what prerequisite skills will lead to later success in Algebra. Although there is some fascinating research that examines how young children are capable of understanding Algebra concepts at a much younger age than once believed. Most recently, Brizuela and colleagues (2012) followed 19 students in grades 3,4, and 5 throughout middle school. The experimental group received weekly algebra lessons plus homework and were compared with a control group. Results showed that students in the experimental group outperformed their peers on algebra assessments given in grades 5, 7, and 8.

If our goal is to promote student understanding of Algebra so that students feel comfortable, using multiple strategies within a representation, analyze situations and making connections between representations than what approaches should teachers incorporate to make algebra meaningful and moreover students successful?

28 comments:

  1. I think that many students are capable of learning Algebra in their earlier years. Students are constantly practicing basic operations with integers until 6th grade when during that time, they can be exposed to algebra. Being exposed to Algebra even in elementary school can help improve understanding. They need to work with variables and understand how to work with them at a younger age so that they can be more comfortable when they see them with deeper understanding in middle school.
    One thing that might help students in middle school or high school can be working with patterns and seeing how the relationship can be represented algebraically. Being able to see this gives working with variable more meaning. Hearing from different student perspectives and seeing different ways to approach problems can further help students use multiple strategies within representations. Guiding questions also seem to be a big motivator in terms to helping students analyze situtations and make connections.

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    1. Exposing algebra to students at a younger age in addition to teaching basic operations with fractions and integrers definitely is one solution to increase student success rate in algebra.

      I do agree that algebra classes have to be structured in such a way that not only works on content, but also builds off ideas heard from others. Group collaboration or teamwork is an integral part of learning algebra. I do not think I can learn algebra on my own. Why should I expect my future students to work on algebra individual basis?

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    2. http://mbamp.ucsc.edu/building-skills/

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  2. I have lots of students who come into math thinking that it is a useless subject and all we need to know is how to add and subtract. What the students do not see is how everything revolves around mathematics. In order to show them the role mathematics plays in all sorts of aspects of life, I must create real-world activities for them to use algebra to solve problems. Showing the application of algebra will address the notion of Algebra being useless. It gets students to think mathematically by getting them engaged into learning about math and being more involved in group projects, presentations, research, and homework.

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    1. Yes! If students can also see how algebra an be applied outside of the classroom, and to real life in relatable situations, they will be more likely to not only use it, but to be motivated to learn it. Having them work on projects and research is a great way to have student branch out and discover for themselves have algebra can be useful outside of following procedures and algorithms.

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    2. I agree that teaching students application of algebra will be more engaging for the students. Furthermore, they would be more interested in algebra. I also agree the students will be more engaged in group projects, presentations, and etc. if algebra was taught in a way that is more applicable

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  3. It seems that students have a lot of difficulty relating abstract mathematical ideas to real world tasks because so little time is spent providing them with legitimate opportunities to use mathematics authentically. Moreover, when these opportunities do arise, they are often covered only shallowly and without sufficient feedback for the students. This promotes the mentality that mathematical applications are arcane and esoteric, while removing opportunities for students to work through the complex problem solving processes involved in troubleshooting an incorrect or inaccurate result.

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    1. Zach, I completely agree. However I don't really see these problems working themselves out soon, considering the state of things now. I would love to hear more about what you might suggest as an answer to this ongoing struggle.

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    2. How did you like CPM? Did you think it did a good job of this? It seems that in geometry this might be easier but I have yet to see a lot of real world application used in Algebra in a fun and motivating way. Students almost want to know how to do the procedure and get the right answer instead of understanding the procedure.

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    1. OH yeah, we totally have to keep it interesting for students. Otherwise we lose their interest the second they walk in the door. It can be hard though sometimes creating lessons that are culturally relevant to all your students. Maybe take turns focusing one each students' cultural histories.

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  5. I really do believe that mathematics has become too abstracted from what it's intended purpose is. In order to teach Algebra better, I think we must teach it for understanding. This means that not only are our students really comprehending the material, instead of guessing and checking, performing banal tasks, and rote memorization, but also that students are personally engaged in the material. This can occur when students are not just passive learners, but active agents in their education, motivated by the curiosity to learn and the need to understand the world around them. The reason we are failing is because it is difficult to mass produce this kind of instructions, for no book can capture within it's pages what it means to inquire into the lives of countless children who come from diverse backgrounds like we see in the United States today. If teachers really want to help their students, they will give them the information they need to succeed, but they also will inspire them to pursue a livelong interest in understanding the world through the lens of mathematics.

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    1. I agree with you Jacki, the problem with algebra is trying to relate it to students' lives and keep them engaged throughout class. I notice that there is a disconnect between algebra and how it relates to real life and thus it is not engaging students and students are falling behind in the subject. As teachers I think we really have to inspire students and show them that algebra is relatable and, even though it is abstract, it is possible to succeed in the subject.

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  6. The second paragraph begins by telling us that "there is little agreement as to what prerequisite skills will lead to later success in Algebra." We are then told that there was success with a group of selected students but what were these weekly algebra lessons that were successful for the students? The article addresses the fact that many students are struggling with algebra and that there is hope but, we are not given any sort of suggestion as to how to make algebra learning possible for students. We have previously read that problems that students can relate to and lots of practice with different types of problems is crucial for student learning. That is why online tools may be useful in the classroom or for students to work with at home for practice. This website has many different resources for beginning algebra students. I thought this game might be fun for working on using variables and plugging in values. http://www.bbc.co.uk/education/mathsfile/shockwave/games/postie.html

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    1. Nichole this looks like a really neat game. It has 3 different levels and is a fun way to practice algebra with your students. Especially if the class of students has access to computers this could be good practice rather than a worksheet

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  7. I think a key component to successful algebra teaching/learning is to keep everyone actively engaged. Direct instruction is only going to take students so far. So on the website below (i'm not sure if ya'll can access it without subscribing) there is an activity called the Murder Mystery Challenge. It combines some algebraic activities and arithmetic to create a fun game built off understanding certain concepts of algebra. Students are less likely to be put off from learning math is it stays fun and exciting. I feel like one of the reasons students fail to succeed in math is because they don't know when they will ever use it or think it is boring and irrelevant. But if we can keep math fun and engaging, students will be more willing to learn.


    http://www.tes.co.uk/ResourceDetail.aspx?storyCode=6068771

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  8. In chapter 4 of Fostering Algebraic Thinking, Mark Driscoll discusses that one of the core principles that teachers can use to foster algebraic thinking in their students is through the use of classroom questioning. I have personally seen through my last placement at Aptos JHS the use of questioning students in a math classroom. I have noticed that math questioning, if used in the proper way, can increase the level of student success in the classroom. If teachers are able to be consistent from the start of the school year with how often they question their students to explain their reasoning and steps then I believe algebra will become more meaningful to them. They will know more than just skills and rote procedures and will have a deeper level of understanding of concepts.

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    1. What specific methods of questioning or protocols for student responses are effective at deepening students' understandings?

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  9. my comment didn't save :(

    I had said that it wasn't a surprise that so many students are unsuccessful at algebra. Algebra is taught in a very abstract and procedural way and students may not always connect why they do perform an operations (other than "the teacher said so"). I think algebra should be taught with word problems in mind from the beginning. Word problems show students how algebra is relatable to real life. We learn algebra in school to apply to our own lives when we're shopping at the grocery store or saving for a new car. I think algebra should be taught with the students' lives in mind and it should be relatable to them. The procedures and standard notation will come with time; I don't think it should be the focus of the entire course.

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  10. I think that the first step to make students comfortable with algebra is exposure starting from an early age. Students need to be introduced to the meaning of algebra and how it connects to their world and future. They need to have time to explore the meaning of a variable and all of its facets. A variable does not just have one definition, teachers need to inform students of a broad definition of a variable and then explicitly break it down. The concept of a variable is fundamental to grade school Algebra yet the majority of students struggle to grasp the concept of a variable. I think it could be possible to introduce it simply but give students examples of how a variable changes in different contexts. If they are introduced to the various ways in which to use a variable, at least they have an idea that it can be used in few different ways, then they can begin working and practicing using a variable in specific contexts. The more understanding they have of what Algebra means and what a variable means the better. They are obviously not going to understand all the ways in which a variable may work in grade school but if they are aware that there are multiple definitions, then they can begin gaining familiarity with specific applications.
    In observing my Watsonville High Algebra connections students I saw that students were able to carry out algebraic rules and manipulate letters and numbers but they struggled to understand what the letters or variables really meant. It is a vast topic but we must try to give students tools to understand a variable, without which they will never really understand algebra.

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  11. In order to make algebra more meaningful, algebra has to be taught in a way that's applicable. For example, writing out word problems that are relevant to them can interest the students to learn algebra. In order for students to be successful in learning algebra, they have to be interested in the topic because they would not be willing to learn something that is not interesting. Teaching students culturally relevant can interest and engage the students to learn algebra. Unfortunately, classrooms these days are too procedural at teaching algebra. This is the main reason why students are not doing so well in algebra.

    http://www.nytimes.com/2012/07/29/opinion/sunday/is-algebra-necessary.html?pagewanted=all

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    1. I like the idea that we should make algebra applicable.

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  12. One approach that teachers can incorporate to making algebra meaningful and moreover students successful is to use technology when teaching algebra. Since students learn best when they are actively engaged in constructing meaning about content that is relevant, therefore when students are developing their own meaning of mathematics, they can make math interesting.
    When using technology to teach algebra, teachers can have students use functions to create different pictures, such as a mountain with -|x|. This way, students are engaged and the lesson is connecting to the students' lives.


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  13. Resource:
    http://www.learner.org/workshops/algebra/

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  14. http://www.youtube.com/watch?v=vi12aITNRts

    video on real life math- snowboarding on slopes!

    Thought it was an interesting video!

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  15. http://faculty.wiu.edu/JR-Olsen/wiu/GAMESand/games/alg.htm

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